Imaging apparatus and method

ABSTRACT

A range of technique for investigating a sample such as obtaining images and/or spectral information are described. The techniques include a method for deriving structural information about a sample as a continuous function of the depth below the surface of the sample, a method for evaluating a part of the structure of a sample located between two interfaces within the sample, and a contrast enhancing method and apparatus which has a quick image acquisition time.

The present invention is concerned with the field of investigating andimaging samples primarily using radiation in the frequency range from 25GHz to 100 THz. This frequency range extends from the mid infrared rangeup to, and including the lower end of the microwave range. This range offrequencies encompasses the Terahertz (THz) range and is generallyreferred to as THz radiation.

Such radiation is non-ionising and, as a result, it is particularly ofuse in medical applications. In any type of medical imaging, radiationis generally reflected from or transmitted through the patient.Radiation in the above frequency range is generally quite heavilyabsorbed in structures having a high water content. Therefore,reflection measurements are believed to be of particular use in suchinvestigations.

Reflection measurements in non-lossy materials have been previouslydemonstrated in EP 0 864 857. This document explains how to performsimple analysis using reflection measurements on non-lossy materialswhich have sharp discontinuities in their refractive index. The positionof the dielectric interfaces within a floppy disc is used to demonstratethe technique.

However, medical samples in general are particularly lossy media, inother words, Terahertz radiation is strongly absorbed in suchstructures. Also, there is a need to be able to determine the structureof sample which does not have sharp discontinuities in its refractiveindex.

The present invention seeks to address the above problems, and in afirst aspect, provides a method of imaging a sample, the methodcomprising the steps of:

-   -   irradiating a surface of a sample with pulse of electromagnetic        radiation, said pulse having a plurality of frequencies in the        range from 25 GHz to 100 THz;    -   detecting said radiation reflected from the sample and deriving        information about the structure of the sample as a function of        depth from the surface of the sample

The above method is ideally intended for use with biological samples.Also, the above method derives information as a continuous function ofthe depth from the surface of the sample. Preferably either therefractive index or the absorption coefficient is derived as a functionof depth from the surface of the sample. The structural information canbe derived as a continuous analytical function of the measured reflectedradiation.

Preferably, the method further comprises the step of obtaining areference signal. The said reference signal is preferably a signal takenwithout the presence of the sample and is preferably obtained byreflecting the radiation off a mirror which has substantially perfectlyreflecting.

The above method uses reflections from the sample in order to obtaininformation about the continuously changing absorption coefficient,refractive index and other structural parameters of the sample. Thetechnique does not rely on the present of sharp discontinuities withinthe sample to derive information about specific regions of the sample,because the method provides an analytical technique for deriving acontinuously changing parameter as a function of depth.

It is possible to perform this analysis using the above method as thewavevector of each frequency component of the THz pulse is dominated bythe absorption coefficient as opposed to the refractive index (which isthe case for lossless media). Preferably the frequency range from 50 GHzto 80 THz is used, more preferably from 100 GHz to 50 THz.

In a second aspect, the present invention provides an apparatus forinvestigating a sample, the apparatus comprising:

-   -   means for irradiating a surface of a sample with a pulse of        electromagnetic radiation, said pulse having a plurality of        frequencies in the range from 25 GHz to 100 THz;    -   means for detecting said radiation reflected from the sample and        deriving structural information about the sample as a function        of depth from the surface of the sample.

Of course, it is possible to study samples which have sharpdiscontinuities in the refractive index using the above method. In bothlossless and lossy media, the signal due to reflection from adiscontinuity in the refractive index such as an internal dielectricinterface or an external surface of the sample can be easily detected.Such a signal usually manifests itself in terms of a large peak in thereflected radiation which can be easily detected.

This reflection data can be used to determine the position of interfaceswithin the same. However, it can also be used to obtain data concerningthe absorption of the sample between the two interfaces. Comparing thesignals from different interfaces in different parts of the sample, isparticularly of use in studying samples where there is some variation inthe absorption of the latter between the two interfaces.

Therefore, in a third aspect, the present invention provides a methodfor studying a sample, the method comprising the steps of:

-   -   irradiating a first part and a second part of a surface of the        sample with electromagnetic radiation having a frequency in the        range from 25 GHz to 100 THz, the first interface being located        closer to the surface than the second interface;    -   detecting the signal due to reflection of the radiation from the        first and second interfaces of the two parts of the sample; and    -   comparing the peak height of the signal from the second        interface with that from the first interface to produce a        connected second interface signal and comparing the connected        second interface signals.

The step of comparing the signal from the first interface with that ofthe second could comprise the step of dividing the peak height of thesignal from the second interface with that from the first or subtractingthe signals. Alternatively, the method could comprise the step ofcomparing the two signals from the two different parts of the samplewith respect to the peak height.

Comparing the peak heights of the signal from the first and secondinterfaces allows any variations in detected radiation due todifferences in the sample position and differences in the sample whichare not between the first and second interfaces to be taken intoaccount.

The above method is particularly of use when looking for an abnormalityin a sample. For example, looking for a skin tumour. In such a sample,there will be a reflection from an interface above the tumour such asthe external surface of the skin, there will also be a reflection froman interface below the skin, for example, the skin/fat interface. Atumour has been shown to absorb THz quite strongly. Therefore, thesignal from the second interface will be weaker in a tumourous regionthan in a non tumourous region.

Hence, one of the parts of the sample is preferably a healthy part whichis used as a reference.

Further, by scanning the THz beam across the skin while looking at therelative height of the signal from the second interface with respect tothe first, it is possible to build up a picture of the extent of thetumour.

The above method is not only limited to looking for tumours. It has beenshown that areas of teeth which have been subjected to dental caries arealso more strongly absorbing than healthy areas of the teeth. Therefore,there will be a marked change in the signal from the second interfacefrom the healthy region of the teeth to the carious region of the teeth.

The above method may comprise the step of looking at many differentparts of the sample, and generating a plot of the corrected second peakagainst the position on the sample. An image of the sample could also bebuilt up by plotting the corrected second peak against the position onthe sample.

To build up a 2D image, an area of the sample is subdivided into pixelsand the reflected radiation form each of the pixels is detected.

The radiation used can be pulsed radiation which comprises a pluralityof frequencies or even continuous wave radiation which has substantiallya single frequency.

In a fourth aspect, the present invention provides an apparatus forgenerating an image of a sample, the apparatus comprising:

-   -   means for irradiating a sample with a pulse of electromagnetic        radiation, said pulse having a plurality of frequencies in the        range from 25 GHz to 100 THz;    -   means for detecting the amplitude of the radiation reflected        from or transmitted by the sample; and    -   means for generating an image of sample using the amplitude of        the radiation detected at a single point in time.

When studying a sample, it is usually desirable to generate and image ofthe sample. Typically, images of the sample have been generated byplotting the maxima or minima of the detected Terahertz radiation.However, it has been found that a better contrast can be obtained bylooking at the THz electric field for a particular time delay.

Therefore, in a fifth aspect, the present invention provides a method ofimaging a sample, the method comprising the steps of:

-   -   irradiating a sample with a pulse of electromagnetic radiation,        said pulse having a plurality of frequencies in the range from        25 GHz to 100 THz;    -   detecting the amplitude of the radiation; and    -   generating an image of sample using the amplitude of the        detected radiation at a particular point in time.

In order to generate an image, it is necessary to measure the THz signalfrom a number of different parts of the sample. Typically, the area ofthe sample which is to be imaged will be subdivided into atwo-dimensional array of pixels and the radiation will be detected fromeach of the pixels. In order to detect radiation from each of thepixels, the sample may be moved relative to the beam of radiation or thebeam may be moved relative to the sample, or both. Alternatively, thewhole area of the sample could be irradiated and the radiationtransmitted through or detected form the area of the sample could bedetected by a CCD camera or the like.

The Terahertz pulse which is used to irradiate the sample will spreadout due to its passage through the sample. As a result, different partsof the pulse will be detected at different times. The leading edge ofthe pulse of a particular features of the pulse, can be thought of asarriving at the detector at a time t=0, then the other parts of thepulse will arrive at the detector with a delay time “t”.

The method of the fifth aspect of the present invention generates animage using a specific ‘t’.

The radiation can be detected at a specific time ‘t’, this isadvantageous as it does not require detecting radiation for every ‘t’and hence the acquisition time of the image is substantially improved.

Alternatively, it may be desirable to detect the radiation for a rangeof ‘t’ and then select a particular “t” in order to generate the image.This allows an image to be scannable using “t” as the scanning variable.Thus, someone using the method could scan the image for various “t”until the image with the best contrast was obtained.

This method could be used for either or both of transmitted data orreflected data.

In a sixth aspect, the present invention provides an apparatus forimaging a sample comprising:

-   -   means for irradiating a sample with a pulse of electromagnetic        radiation, said pulse having a plurality of frequencies in the        range from 25 GHz to 100 THz;    -   means for detecting the amplitude of the radiation reflected        from or transmitted by the sample; and    -   means for generating an image of sample using the amplitude of        the radiation detected at a single point in time.

The apparatus preferably further comprising means for displaying aplurality of images generated from different time points. Morepreferably, the apparatus comprises optimising means for optimising theimage using the variable parameter of the delay time.

The present invention will now be described with reference to followingpreferred non-limiting embodiments:

FIG. 1 shows a schematic imaging system in accordance with an embodimentof the present invention;

FIG. 2 shows an example of a generation section for use with the imagingsystem of FIG. 1;

FIG. 3 shows an example of a detection section for use with the imagingsystem of FIG. 1;

FIG. 4 shows a further example of a generator for use with the imagingsystem of FIG. 1;

FIG. 5 shows a further example of a detector for use with the imagingsystem of FIG. 1;

FIG. 6 shows a schematic trace of a pulse detected by the imaging systemof FIG. 1;

FIG. 7 shows an image of a skin carcinoma produced in accordance with anembodiment of the present invention;

FIGS. 8a and 8b shows two images of a tooth produced using a method inaccordance with an embodiment of the present invention;

FIG. 9a shows a visible image of a slice through a tooth, FIG. 9b showsa typical THz time domain trace for a tooth, FIGS. 9c, d and e show timeslice images for the tooth at delayed times −0.08 ps, 0.1 ps and 3.34ps;

FIG. 10a to 10d show four images of time slices through the tooth shownin FIG. 9 a;

FIG. 11a shows a visible image of a tooth, FIG. 11b shows an absorptionimage of the tooth of FIG. 11a , FIG. 11c shows a time of flight imageof the tooth of FIG. 11a , FIGS. 11d to 11f show time slices of thetooth of FIG. 11a for times −0.1 ps, 2.4 ps and 3.1 ps respectively;

FIG. 12a shows a visible image of a tooth, FIG. 12b shows the absorptionimage of that tooth, FIG. 12c shows a time slice through that tooth andFIG. 12d shows an image of the tooth plotting the time of the maximumpeak of the electric field;

FIG. 13 shows a visible image of a tooth and a THz signal from thetooth;

FIG. 14 shows a visible image of a tooth and two THz traces of diseasedand healthy parts of the tooth;

FIG. 15 is a schematic of skin and shows a schematic signal from theskin; and

FIG. 16 shows a schematic layer structure of a sample which can beinvestigated using a method in accordance with an embodiment of thepresent invention;

FIG. 17 shows a schematic of a variation of the imaging system of FIG.1;

FIG. 18a shows a typical signal measured by the apparatus of FIG. 17 andFIG. 18b shows the corresponding THz power spectrum;

FIG. 19 shows a schematic of the layers of skin and an input andreflected pulses;

FIG. 20 is a visible image of a human arm and hand indicating points onthe arm and hand which are measured to produce the results in thefollowing figures;

FIG. 21a is a plot of a time domain THz waveform measured from theforearm and compared with that from air and water; FIG. 21b is a THzwaveform comparing the reflected pulse from the forearm, wrist and palm;

FIG. 22a is a 1 cm by 1 cm image of the side of the hand of FIG. 20;FIG. 22b is a time slice image of the hand;

FIG. 23a is an image of the palm of the hand of FIG. 20, FIG. 23b showsthe corresponding data from the edge of the subject's palm;

FIG. 24a is a comparative plot of a THz measurement of the forearm ofFIG. 20 under different wetting conditions; and FIG. 24b shows plots ofmeasurements of the palm and forearm before and after application ofglycerine solution; and

FIG. 25a is a comparative plot of the changing characteristics of aforearm over a 15 minute period, and FIG. 25b is a plot of the maximasof the traces of FIG. 25a against time.

FIG. 1 shows a basic THz imaging system. The system can be simplifiedinto three main sections, a generator 31, an imaging section 33 and adetection section 35. THz radiation is generated in the generatingsection 31 by using a THz emitter which is supplied by a visible pulsedlaser 37.

A THz beam 39 is emitted from generation section 31 and is directed ontosample 41 of the imaging section 33. The THz beam 39 is then reflectedfrom sample 41 and directed via further optics 45 into the detectionsection 35. The THz beam which is reflected from the sample 41 is beam39.

The detection section reads the information carried in the detected THzsignal via a visible light signal and AC Pockels effect. The visiblelight can be obtained from laser 37 via beam splitter 47. Laser 37 is aTi:Sapphire laser which typically produces wavelengths in the range of900 nm to 350 nm, with a pulse width of 50 fs and a repetition rate of82 MHz.

Beam splitter 47 splits the beam into a reference beam 55 and a beam forTHz generation. A time delay is added to the reference beam 55 via timedelay line 34. Varying the time delay via the time delay line allows thephase of the reference beam to be varied with respect to that of the THzbeam 39. This is used in detecting the THz beam in detection system 35.The system (e.g. the control of the sample 41 movement, the time delay34 and the detected signal processing) is controlled by computer 36.Details of the AC Pockels effect will be described with reference toFIG. 3.

FIG. 2 shows a generator which can be used with the imaging system ofFIG. 1 Here, for simplicity, details of the detection part of the systemwill be omitted. These will be described with reference to FIG. 3.

FIG. 2 shows a THz generator using a frequency conversion member whichmay be a crystal which non-linear properties of the like such as ZnTe.The radiation used to generate the THz radiation via frequencyconversion member 315. Radiation is supplied to frequency conversionmember 315 from Ti:Sapphire crystal 317. Ti:Sapphire crystal 317 emits apump beam, which comprises pulses of radiation, in response to radiationwith laser driving beam 319. In order to provide efficient lasing, it isdesirable to continually reflect the pump beam 307 onto Ti:Sapphirecrystal 317. Therefore, the lasing crystal 317 is typically providedwithin a lasing cavity.

The driving beam 319 is directed onto crystal 317 using mirrors M1 andM2. The driving beam 319 can pass through mirror M3 and onto lasingcrystal 317. The driving beam 319 which is not absorbed by crystal 317,is emitted through mirror M4. Mirror M4 serves to reflect any radiationback onto the lasing crystal 317. This radiation is then reflected viamirror M3 onto mirror M5 and onto output coupler 321. Output coupler 321serves to reflect the pump beam 307 onto the frequency conversion member315 to produce Terahertz radiation. The pump beam is focused ontofrequency conversion member 315 via lens L1. Any radiation which istransmitted through the frequency conversion member 315 is reflectedback through the frequency conversion member 315 by mirror M6. Thisradiation then impinges on output coupler 321.

Output coupler 321 transmits terahertz radiation, but it reflects mostof the pump beam back onto mirror M5, which in turn reflects theradiation back onto the lasing crystal 317 via mirror M3. In otherwords, the lasing crystal 317 and the frequency conversion member 315are all located within the same lasing cavity defined by mirror M6, theoutput coupler and mirrors M5, M3 and M4. The pump beam 307 iscontinuously reflected within this cavity to efficiently generate thepump beam and the THz beam.

The THz beam 53 which is emitted from output coupler 321 is directedinto the imaging section 33 and onto sample 41 via THz imaging optics(not shown). The sample 41 is located on a motorised X-Y translationstage (not shown) so that the whole sample 41 can be imaged. (The x-yplane is orthogonal to the beam axis). The THz radiation carrying theimaging information from the sample is reflected into the THz detectionsystem 35 via THz imaging optics 45.

Output coupler 321 transmits some visible radiation 55 as well as THzradiation as a reference beam 55. Imaging and electro-optic detectioncan be performed inside a single nitrogen-purged unit.

The sample 41 is mounted on a X-Y motorised translation stage (notshown) which is controlled by a PC computer (not shown). Each section(pixel) of the object may then be imaged. To improve the spatialresolution of the technique, off-axis parabolic mirrors, condensercones, and lenses may be used to focus the beam to a diffraction limitspot. By mounting the sample in the near field of a condenser cone, thediffraction limit may be overcome and spatial resolution of about 50 μmmay be achieved. The imaging system can function with or without suchobjects depending on the nature of the object to be imaged and thenature of the detection circuit.

FIG. 3 shows the detection system in detail. The THz beam 39 carryingthe imaging information and a visible light beam 55 are inputted intothe THz detection system. The visible light beam 55 acts as a referencebeam which is incident on the detection crystal 73. The reference beam55 is linearly polarised and the polarisation is orientated such that ithas components along both the ordinary and extraordinary axis of thedetection crystal 73. Each of the axes has distinct refractive indicesn_(o) and n_(e) along the ordinary and extraordinary axis of the crystal73 respectively. In the absence of a second (THz) radiation beam 39, thelinearly polarised reference beam 55 passes through the detectioncrystal 73 with negligible change in its polarisation.

The applicant wishes to clarify that the angle Θ through which thepolarisation is rotated by is negligible. However, the linearlypolarised beam can become slightly elliptical. This effect iscompensated for by a variable retardation waveplate, e.g. a quarterwaveplate 81.

The emitted beam 77 is converted into a circularly polarised beam 83using quarter wave plate 81. This is then split into two linearlypolarised beams by a Wollaston Prism 79 (or equivalent device forseparating orthogonal polarisation components) which directs the twoorthogonal components of the polarised beam onto a balanced photodiode85. The balanced photodiode signal is adjusted using wave plate 81 suchthat the difference in outputs between the two diodes is zero.

However, if the detector 73 also detects a secondary beam 69 (in thiscase a beam with a frequency in the THz range) as well as a referencebeam, the angle Θ through which the polarisation is rotated by is notnegligible. This is because the THz electric field modifies therefractive index of the visible (fundamental) radiation along one of theaxes n_(e), n_(o). This results in the visible field after the detector73 being elliptical and hence the polarisation components separated bythe prism 79 are not equal. The difference in the voltage between theoutput diodes gives a detection voltage.

The reference beam 55 and the THz beam 39 should stay in phase as theypass through the crystal 73. Otherwise the polarisation rotation Θ isobscured. Therefore, the detection crystal 73 has phase matching meansto produce a clear signal.

Other types of generator may also be used. FIG. 4 illustrates aso-called photoconductive emitter. The emitter comprises a member 91comprising a semiconductor such as low temperature GaAs, GaAs, Si onSapphire etc. The semiconductor member has a pair of electrodes 93 a and93 b located on its surface. The electrodes 93 a and 93 b are connectedto a power supply such that a field can be generated between the twoelectrodes 93 a and 93 b.

The simplest electrode arrangement is show in FIG. 4. However, theelectrodes may be triangular and arranged in a bow-tie shape, aso-called bow-tie antenna or they may be interdigitated electrodes atthe centre of a bow tie or spiral antenna. Alternatively, such designsmay be incorporated into transmission lines on the chip.

The semiconductor member is irradiated by a pump beam which is a pulseof radiation (about 70 fs) of the type which can be emitted by laser 37.The pulse comprises at least two frequencies ω₁ and ω₂, the differenceof which gives a frequency in the THz regime. The pump beam impinges onthe semiconductor member 91 on the part of its surface between theelectrodes 93 a and 93 b, i.e. where the field is applied. The beatingof the two visible or near-infrared frequencies in the non-linear regionof the semiconductor member between the two electrodes 93 a and 93 bresults in the emission of THz radiation from the semiconductor member91. The semiconductor member 23 is provided with a lens 95, which may beof a hemispherical or other design, on its surface which is opposite tothat of the surface with the electrodes, to allow the emission of a beamof THz radiation.

FIG. 5 shows a further example of a detector which may be used with theimaging system of FIG. 1. This type of detector is known as aphotoconductive detector and comprises a detection member which may be,for example, GaAs, Si on Sapphire etc. The THz radiation is incident onthe back surface of the detection member 96. The radiation is collectedby lens 98 which may be hemispherical or have another shape. On theopposing side of the detection member 96 is located a pair of electrodes97 a and 97 b. The region between these two electrodes 97 a and 97 b isilluminated by radiation of the visible or near infrared range.

The near-infrared/visible radiation illuminates the surface of thedetector between the electrodes 97 a and 97 b. The Terahertz radiationwhich is collected by lens 98 induces a photocurrent through the regionbetween the electrodes 97 a and 97 b which is being illuminated by thevisible/infrared radiation. The current which can be detected by theelectrodes is proportional to the strength of the THz field.

The electrode 97 a, 97 b may be of a simple diode formation embedded ina transmission line. Alternatively, they may be triangular and arrangedin the shape of a bow-tie to from a so-called bow-tie antenna. They mayalso be interdigitated electrodes at the centre of a bow-tie or spiralantenna.

FIG. 6 shows a schematic trace of a THz pulse which has been reflectedfrom the sample using the type of apparatus which is shown for theexample in FIG. 1.

An oscillating electric field is plotted on the y axis against timealong the x-axis. Typically, methods of extracting information from thetrace have used either the position in time of the maxima of theelectric field (T₁) or the position in time of the minima of theelectric field (T₂).

As it can be seen from FIG. 6, the magnitude of the measured electricfield changes considerably with time. There is only a small timedifference between T₁ and T₂. When looking at an area of the sample, atrace like the one shown in FIG. 6 will be obtained for each point ofthe sample. The trace will change from point to point or pixel to pixeldependent on the composition of the sample.

FIG. 7 shows a reflection image of a skin carcinoma. FIG. 7a shows theTHz image and FIG. 7b shows the image using visible radiation.

To generate the image in FIG. 7a , only reflected radiation from asingle delay time i.e. a single point on the x axis of FIG. 6, isplotted. The delay time may be the maxima of the electric field in someparts of the sample or the minima of the electric field in other partsof the sample. It can be seen that this image shows good contrast. As itis only necessary to measure the THz signal at a particular delay time,there is no need to continually sample the whole of the THz pulse.Therefore, the image can be produced using a much shorter acquisitiontime. Also, the image requires less processing.

FIGS. 8a and 8b show two images generated using THz radiation of atooth. FIGS. 8a and 8b were produced in a similar manner to that of FIG.7. In other words, the image was taken for a single time delay. The timedelay chosen was 0 picoseconds for FIG. 8 a.

FIG. 8b shows the same tooth of FIG. 8a , however, here the time delayis 6.99 picoseconds. It can be seen that the image in FIG. 8b is farsharper than that of FIG. 8a . The optimum image can be obtained bychoosing the correct time delay.

FIG. 9a shows a visible image of a tooth. The tooth is actually a slicethrough a tooth, the various regions such as the enamel-dentine region201 and the pulp cavity region 203 can be distinguished. The enameldentine region 201 has decayed due to caries in regions 205 and 207.

FIG. 9b shows four THz traces plotted as amplitude of detected THzsignal against time delay for three regions of the tooth and a referencesignal. It can be seen that the reflected detected THz is quitedifferent for the various regions. For example at peak 209, the signaltaken in the enamel region (E) of the tooth is seen to dominate.Similarly, at peak 211, the dentine signal (D) is seen to dominate. Atpeak 213 the signal due to caries (C) dominates the trace. The referencesignal (R) is generally seen to be the lowest peak.

By looking at the detected THz signals for different delay times, it ispossible to distinguish differences between the different parts of thetooth.

FIGS. 9c, 9d and 9e show images of the tooth taken at times −0.08 ps,0.1 ps and 3.34 ps. These times correspond to the x axis of the FIG. 9b. The trace as seen in FIG. 9b will have to gathered for every part ofthe tooth of FIG. 10a , but only for a single point on the x-axis,looking at a particular delay time is referred to as taking a time slicethrough the spectra.

The decayed regions 205 and 207 can be seen in all of FIGS. 9c, 9d and 9e.

FIGS. 10a to 10d show further time slices of the tooth of FIG. 9a ,which have not been optimised to illustrate carious regions 205 and 207.Comparing the time slices of FIGS. 10a to 10d with those of FIGS. 9c to9e , it can be seen that the contrast especially in the caries region205 and 207 is far more marked in FIGS. 9c to 9e as opposed to FIGS. 10ato 10 b.

FIG. 11 shows a range of different images for a tooth. The tooth used togenerate the images of FIG. 11 is different to the tooth used togenerate the images of FIG. 9. Here, a visible image of a slice throughthe tooth is shown in FIG. 11a . It can be seen that there is no decayin this tooth. FIG. 11b shows a THz absorption image of the tooth ofFIG. 11a . This is just simply obtained by measuring the electric fieldfor each point on the tooth at the detector. The absorption image hereis generated from all of the frequencies of the incident pulse of THzradiation, i.e. it is a panchromatic image.

FIG. 11c is a so-called time of flight image. Returning momentarily backto FIG. 9c which shows the THz trace, it can be seen that there is amaxima of the electric field. The time of flight image looks at thismaxima and plots the change in temporal position of the this maxima foreach point in the area of the sample being imaged.

As with the absorption and visible images, the pulp cavity 203 and theenamel dentine region 201 can be easily distinguished.

FIGS. 11d, 11e and 11f show time slices (similar to those described forFIGS. 9c to 9Ee) for delay times −0.1 ps, 2.4 ps and 3.1 psrespectively. It can be seen that the contrast of the enamel dentineregion 201 with the pulp cavity 203 changes dramatically between thethree figures. Also, there is no indication of caries in any of theenamel regions in all of the time slices.

FIG. 12 shows a further tooth. FIG. 12a shows a visible image of thetooth, again the enamel dentine region 201 and the root/pulp cavity 203can be easily determined. The tooth has a caries region 205 which cannot be easily seen on the visible image 203.

FIG. 12b shows the absorption image which is obtained in the same way asFIG. 11B.

FIG. 12c shows a time slice. In both FIGS. 12c and 12b , the cariesregion 205 can be easily seen. FIG. 12d shows an image which is plottedby plotting the maxima of the electric field for each point of thesample which is irradiated. The enamel dentine region 201 can be seen.However, the caries region 205 is very weak and much weaker for thatthan the time slice shown in FIG. 12c . The acquisition time for thetime slice can be very fast because it is only necessary to detect thereflected THz for a single point in time.

FIG. 13 shows a further image of a tooth. FIG. 13a shows a visible imagewhereas FIG. 13b shows a single plot of the THz reflected electric fieldagainst time. The THz image is taken along path 101 of the tooth. Thereare three strong features in the reflected THz. The first peak 103 isdue to reflection of the THz from the enamel/air surface. The secondpeak 105 is due to reflection of the THz from the enamel/dentineinterface e-d in the tooth. The third and weakest reflection is due tothe dentine/pulp cavity interface d-p of the tooth.

FIG. 14a shows a visible image of a slice of a tooth. The tooth has ahealthy region 109 and a decayed region 111. FIG. 14b shows a THz pulsein the time domain measured in the healthy region 109. FIG. 14c shows aTHz pulse measured in the time domain for the unhealthy region which isdecayed due to caries 111. Returning to the visible image of the toothslice in FIG. 14a , two interfaces can be seen. The first is theenamel/air interface 113, the second is the enamel/dentine interface115. In the THz trace, the healthy region two peaks 117 and 119 can beeasily distinguished. The upper peak 117 is believed to be due to thereflection of the THz at interface 113, the second peak 119 is due tothe reflection of THz at interface 115.

In the THz pulse of the unhealthy region, the peak due to the reflectionfrom interface 113 is seen to be of almost the same height as thecorresponding peak in FIG. 14 b.

However, the second peak which is due to the reflection from interface115 is seen to be much smaller. This is because a region of the toothwhich is decayed due to caries absorbs THz far more strongly than aregion which has not decayed. Hence, less of the THz penetrates as faras interface 115 and THz which is reflected from this interface is alsomore strongly absorbed than in the case of healthy teeth. Hence, peak119 is considerably reduced in the trace of the unhealthy region.

Regardless of whether or not the tooth is healthy, the height of thepeak from interface 113 should be identical in both traces b and c.However, due to their different positions on the tooth, possibly dirt onthe surface of the tooth, they will almost always be different,therefore, in order to detect the presence of caries, the ratio of peakheights 117 and 119 between a healthy region and an unhealthy regionshould be compared.

This type of analysis does not only apply to teeth. FIG. 15 shows aschematic of a healthy area of skin and an unhealthy area of skin. FIG.15b shows the THz pulse which has been reflected from a healthy regionof the skin, FIG. 15c shows a THz pulse in the time domain which hasbeen reflected from an unhealthy portion of the skin.

In FIG. 15a , a skin/air interface 121 is shown and a skin/fat interface123. There is a healthy area 125 and an unhealthy area 127 whichcontains tumour 129. FIG. 15b shows a THz time domain pulse for thehealthy area 125. The first peak 131 is due to reflection from interface121. The second peak 133 is due to reflection from skin/fat interface123. FIG. 15c shows a similar trace except here, it is taken inunhealthy region 127. The size of peak 131 remains virtually the same.However, the size of peak 133 is substantially reduced due to theabsorption by the tumour 129.

By plotting the ratio of the reflection from the first interface 121 tothe second interface 123, across the skin, the lateral extent of thetumour can be determined as shown in FIG. 15 d.

It is also possible to obtain information about the depth of a sampleusing reflection measurement which does not have particularly stronglydefined interfaces. Lossy materials, such as biological samples have arelatively large absorption coefficient which dominates how radiation isreflected from the sample.

FIG. 16, shows a THz pulse incident on a sample. The THz pulsepropagates in the x-direction and is scattered (reflected) into acounter-propagating, or reflected, pulse by the object.

To simplify matters, the following analysis will only consider onespatial dimension (x) (i.e. for the case of a collimated THz beam path).It will also be assumed the object is uniform in the y-z plane over thedimensions of the THz beam. Given the 1-D analysis described here toprovide information on the structure of the object in the x-direction,the variation of the object in the y-z directions may be obtained byscanning the object through the THz beam in the y-z plane (or,alternatively, scanning the THz beam over the object).

The analysis can be used to determine both how the absorption and therefractive index spatially varies within the sample. In practice, boththe absorption coefficient and the refractive index vary also withfrequency. The following analysis assumes that the frequency response ofthe refractive index is known and also that the absorption coefficientdoes not vary with frequency.

Since the electric field due to the reflected THz pulse may only bemeasured at discrete points in time, all the integral transforms belowmust be replaced by the appropriate discrete transform in order tooperate on the finite dataset.

The incident and reflected THz pulses are characterised by electricfields T(x,t) and R(x,t) respectively. The quantities in bracketsindicate that T and R are both functions of position, x, and time, t. Itwill be assumed that all electric fields are polarised along a similaraxis perpendicular to the x-direction and hence they can be written asscalar quantities (i.e. ignore directional dependence):

$\begin{matrix}{{T\left( {x,\mspace{11mu} t} \right)} = {\int_{- \infty}^{\infty}{{{T_{\omega}(x)} \cdot e^{{- i}\;{\omega \cdot t}} \cdot \ d}\;\omega}}} \\{{R\left( {x,\mspace{11mu} t} \right)} = {\int_{- \infty}^{\infty}{{{R_{\omega}(x)} \cdot e^{{- i}\;{\omega \cdot t}} \cdot \ d}\;\omega}}}\end{matrix}$where i is the imaginary unit √{square root over (−1)}. The waves arewritten in their complex form; the true electric fields are obtained bytaking the Real part of the complex waves. T_(ω) and R_(ω) are thecomplex amplitudes of the respective incident and reflected waves ateach frequency component f where f=2π/ω and these quantities are alsofunctions of position, x. The ω-subscripts indicate that a quantity is afunction of ω, k is the wavevector of each frequency component of thewave and is defined by

$k = {\frac{n_{\omega}\omega}{c} + {i\frac{\alpha_{\omega}}{2}}}$where c is the speed of light in a vacuum, n_(ω) and α_(ω) are therefractive index and absorption coefficients of the object at angularfrequency ω. Thus both n_(ω) and α_(ω) may be functions of position andfrequency. These are the materials parameters which characterise theobject.

The propagation and coupling of energy between the incident andreflected waves is described by two, coupled 1^(st) order differentialequations (easily derived from Maxwell's Equations):

$\begin{matrix}\begin{matrix}{{\frac{\partial T_{\omega}}{\partial x} + {i\; k\; T_{\omega}}} = {\frac{d\; k}{d\; x}\frac{1}{2k}R_{\omega}}} \\{{\frac{\partial R_{\omega}}{\partial x} - {i\; k\; R_{\omega}}} = {\frac{d\; k}{d\; x}\frac{1}{2k}T_{\omega}}}\end{matrix} & {{Eq}.\mspace{11mu} 1}\end{matrix}$

The left-hand-sides of the above equations describe the propagation ofthe two counter-propagating waves. The right-hand-sides provide the‘coupling’ terms which transfer energy from one beam to the other in thepresence of a scattering potential. In this case, the scatteringpotential is provided by a spatially varying wave-vector, k. I.e.

$\frac{d\; k}{d\; x}$must be non-zero for photons to be transferred from the incident wave tothe reflected wave and vice versa. Where

${\frac{d\; k}{d\; x} = 0},$there is no coupling between the beams and the incident and reflectedwaves propagate independently.

In a lossy, dispersive medium α≠0 and where n_(ω) is frequencydependent.

It will be assumed that the scattering potential is provided by aspatially varying coefficient, Δ(x) such thatk=k′Δ

${\frac{1}{k}\frac{d\; k}{d\; x}} = \frac{d\;\Delta}{d\; x}$where k′ is the spatial average of k and k′ is independent of x. (k′remains a function of ω, while Δ is independent of ω).

In order to derive spatial information (i.e. information on how Δ varieswith respect to x), it is necessary to know the spectral characteristicsof the material in advance (i.e. to know how n_(ω) depends on ω). Afunctional form of n_(ω)(ω) and also the coefficient α are assumed. Forthe purposes of imaging, this may be calculated from the spatial averageTHz reflectivity of the sample (i.e. such that structural information isaveraged out). The derivation of the spectral characteristics of asample by THz reflection has been described elsewhere in the literatureand will not be reproduced here.

For a lossy medium where α/2>>nω/c (such as water-based biologicalmedia) a Real spatial variation in Δ is due to a spatial variation inthe absorption coefficient of the medium. Previously, only a spatialvariation in the refractive index have been considered.

Furthermore, it is assumed that the spatial variation of k is muchsmaller than the absolute value of k i.e.

${\frac{d\; k}{d\; x} ⪡ k},$and that the loss of energy from the incident wave due to reflection ismuch smaller than the loss due to absorption. These conditions areappropriate to most biological samples or sample of high water content.In this approximation, the spatial dependence of the incident wave isindependent of the spatial variation of k and is given by

${T_{\omega}(x)} = {T_{\underset{\omega}{x} = 0} \cdot e^{{- i}\; k^{\prime}s}}$where T_(x=0) is the amplitude of the incident electric field atposition x=0 and is a function of ω.

The spatial dependence of the reflected wave may now be described by asingle differential equation:

$\begin{matrix}{\begin{matrix}{{\frac{d\; R_{\omega}}{d\; x} - {i\; k^{\prime}R_{\omega}}} = {\frac{1}{2}\frac{d\;\Delta}{d\; x}T_{\underset{\omega}{x} = 0}e^{{- i}\; k^{\prime}s}}} \\{= {\left( {\frac{1}{2}\frac{d\;\Delta}{d\; x}{T_{\underset{\omega}{x} = 0} \cdot e^{{- \frac{\alpha}{2}}x}}} \right)e^{{- i}\frac{n_{\omega}\omega}{c}x}}} \\{= {T_{\underset{\omega}{x} = 0}{F(x)}e^{{- i}\frac{n_{\omega}\omega}{c}x}}}\end{matrix}{{{with}\mspace{20mu}{F(x)}} = {{\frac{1}{2}\frac{d\;\Delta}{d\; x}} = e^{{- \frac{\alpha}{2}}x}}}} & {{Eq}.\mspace{11mu} 2}\end{matrix}$

Equation 2 may be solved (by the method of Laplace transformation, forexample), to obtain R_(ω):

${R_{\omega}(x)} = {T_{\underset{\omega}{x} = 0}{\int_{x^{\prime} = 0}^{\infty}{{{F\left( x^{\prime} \right)} \cdot e^{i\frac{n_{\omega}\omega}{c}{({x - {2x^{\prime}}})}}}\ d\; x^{\prime}}}}$

Since it is necessary to measure the reflected wave at one point, we setx=0 to get

$\begin{matrix}{R_{\underset{\omega}{x} = 0} = {T_{\underset{\omega}{x} = 0}{\int_{x^{\prime} = 0}^{\infty}{{{F\left( x^{\prime} \right)} \cdot e^{{- i}\frac{n_{\omega}\omega}{c}2x^{\prime}}}\ {dx}^{\prime}}}}} & {{Eq}.\mspace{14mu} 3}\end{matrix}$

This expression may be inverted to obtain F(x) under the assumption thatF is independent of

$\left( \frac{n_{\omega}\omega}{c} \right)$This is not strictly true for systems where the absorption is a functionof frequency. By making this assumption the analysis is simplified; theeffect of the finite frequency dependence of the absorption coefficientis primarily to limit the spatial resolution (in the x-direction) of thefinal result, at frequencies where the frequency dependence issignificant.

By inverse Fourier transformation of Equation 3 we get

$\begin{matrix}{{F(x)} = {{\frac{1}{2}\frac{d\;\Delta}{dx}e^{{- \frac{\alpha}{2}}x}} \approx {\frac{1}{2\;\pi}{\int_{- \infty}^{\infty}{\frac{R_{\underset{\omega}{x} = 0}}{T_{\underset{\omega}{x} = 0}}e^{i\frac{2n_{\omega}\omega}{c}x}\ {d\left( \frac{2n_{\omega}\omega}{c} \right)}}}}}} & {{Eq}.\mspace{14mu} 4}\end{matrix}$

The spatial dependence of the parameter Δ(x) contains the structuralinformation about the object which we are trying to deduce. This isobtained by rearranging Equation 4 and integrating over the position, x.

$\begin{matrix}{{\Delta(x)} = {\frac{1}{2\;\pi}{\int_{x = 0}^{\infty}{2e^{{- \frac{\alpha}{2}}x}\ {\int_{\omega = {- \infty}}^{\infty}{\frac{R_{\underset{\omega}{x} = 0}}{T_{\underset{\omega}{x} = 0}}{{e^{i\; 2n_{\omega}\frac{\omega}{c}}\ \left( {\frac{2n_{\omega}}{c} + {\frac{2\omega}{c}d\;\frac{n_{\omega}}{d\;\omega}}} \right)} \cdot d}\;{\omega \cdot {dx}}}}}}}} & {{Eq}.\mspace{14mu} 5}\end{matrix}$

The factor R_(x=0, ω) is obtained by Fourier transform of the measuredreflected THz electric field, R(t) (i.e. as measured at point x=0,corresponding to the surface of the medium or sample):

$R_{\underset{\omega}{x} = 0} = {\frac{1}{2\;\pi}{\int_{t = 0}^{\infty}{{R(t)}\ {e^{i\;\omega\; t} \cdot {dt}}}}}$

The factor T_(x=0, ω) is obtained by Fourier transform of a referenceTHz pulse. The THz reference pulse may be obtained by measuring the THzpulse reflected off a sample of known reflectivity such as a silvermirror, for example. The THz pulse reflected from a silver mirror is anexact replica of the incident THz pulse i.e.T ^(silver)(t)=R ^(silver)(t)

A similar transformation is performed on T(t):

$T_{\underset{\omega}{x} = 0} = {\frac{1}{2\;\pi}{\int_{t = 0}^{\infty}{{T(t)}{e^{i\;\omega\; t} \cdot {dt}}}}}$

In practice, the incident THz pulse must have a finite bandwidth; thatis, T_(x=0, ω) will drop below the noise-level of the measurementapparatus at frequencies above some threshold, ω_(max). Similarly,T_(x=0, ω) will drop below the measurement noise at frequencies belowsome minimum threshold, ω_(min). In order to exclude artefacts due tonoise where T_(x=0, ω) has become small, we included a windowingfunction W(ω). This function has the property that it drops to zero atboth high and low frequencies faster than T_(x=0, ω).

For example, we may choose W_(ω)=W(ω) to be a square-pulse function:

$\begin{Bmatrix}{{{W(\omega)} = 1};{\omega_{\min} < \omega < \omega_{\max}}} \\{{{W(\omega)} = 0};{{all}\mspace{14mu}{other}\mspace{14mu}\omega}}\end{Bmatrix}\quad$

The final result is

$\begin{matrix}{{\Delta(x)} = {\frac{1}{2\;\pi}{\int_{x = 0}^{\infty}{2e^{\frac{\alpha}{2}x}\ {\int_{\omega = {- \infty}}^{\infty}{\frac{R_{\underset{\omega}{x} = 0}}{T_{\underset{\omega}{x} = 0}}W_{\omega}{{e^{i\; 2n_{\omega}\frac{\omega}{c}}\ \left( {\frac{2n_{\omega}}{c} + {\frac{2\omega}{c}\frac{{dn}_{\omega}}{d\;\omega}}} \right)} \cdot d}\;{\omega \cdot {dx}}}}}}}} & {{Eq}.\mspace{14mu} 6}\end{matrix}$

$\frac{{dn}_{\omega}}{d\;\omega}$may be calculated directly from the previously determined functionalform of n_(ω).

Equation 6 constitutes the main result. Δ(x) is obtained by numericalevaluation of Equation 6, once all the constituent factors have beendetermined. Since Δ is complex either the real or the imaginary part ofthe function may be plotted to form an image, or some combination. Aobtained in this way is considered only an approximation to the exactstructural form of the sample, in view of the approximations describedabove.

FIG. 17 shows an imaging system which is similar to FIG. 1. To avoidunnecessary repetition, like reference numerals will be used to denotelike features. A Ti:Sapphire laser system 37 (coherent Reg A9000)operating at a 250 kHz repetition rate is used to provide the inputradiation. The radiation is split using beam splitter 47 to produce aprobe beam 55 and a pump beam 39. The pump beam is first directedthrough a 1 ns delay line 401. This is a static delay line and is usedto make fine adjustments to the path length. The pump beam is thendirected into a 150 ps scanning delay line 403 having a scanningfrequency of 20 Hz. The scanning delay line has a linear-position outputso that it is possible to know the position of the delay line when eachmeasurement is taken. The pump beam is then fed through a 64 kHzmodulator 405 which chops the beam at this frequency in order to providea frequency for detection using lock-in techniques.

The pump beam 39 is then directed onto GaAs antenna 407. The antenna isbiased to 1.1 kV and average powers of over 1 nW are generator. The pumpbeam 39 power delivered to the antenna is 1 to 2 μJ. Such antennas aredescribed in detail in J. T. Darrow and B. B. Hu and X.-C. Zhang and D.H. Auston 1990, Optics Lett., 15(6), pages 323-5, Z. G. Lu and P.Campbell and X.-C. Zhang, 1997 Appl. Phys. Lett., 71(5), pages 593-5,and G. Mouret and W. Chen and D. Boucher and R. Bocquet and P Mounaixand D. Theron and D. Lippens, 1998, Microwave and optical technol.lett., 17(1), pages 23-7. In the specific antenna of this example, anacrylic anti-corona coating is used and a 100 KΩ series resistor tosuppress dielectric breakdown of the device and to reducepower-dissipation in the GaAs. The emitted THz pulses are guided fromantenna 407 via off-axis parabolic mirror 409 onto sample 411. Thereflected radiation from the sample is then collected via parabolicmirror 413 and directed into detector 35. The detector is of the EOStype described with reference to FIG. 3. In the specific example of FIG.17, the reflected THz beam is directed onto 1 mm thick ZnTe crystalcolinearly with the probe beam 55.

Where non-planar soft materials, for example, human skin are measured, aquartz window is used in order to flatten the skin to improve the image.

FIG. 18a shows a typical plot of THz signal (arbitrary units) againstdelay time of the optical pulse (measured by the 150 ps scanning delayline) which can be obtained using the apparatus of FIG. 17. The smalleroscillations after the main pulse are due to atmospheric water-vapourabsorption and dispersion in the THz beam path. A small signal can beseen at 10 ps after the main pulse due to back-reflections from the GaAsantenna substrate. The signal-to-noise ratio for a typical THz waveform(measured with a metallic mirror in place of a sample) is greater than6000 to 1 for a single delay line scan. This typically has anacquisition time of 50 ms.

The bandwidth envelope which is obtained from Fourier transforming thetime domain waveform of FIG. 18a is shown in FIG. 18b . FIG. 18bactually shows the THz power spectrum. The spectrum peaks at 300 GHzwith useful power to over 3 THz. The large THz throughput of the systemallows the acquisition time for 3D data sets to be reduced to just a fewminutes.

FIG. 19 is a schematic of the outermost layers of human skin. Thestratum corneum 421 being the outermost layer, the middle layer is theepidermis 423 and the innermost layer of interest in these experimentsis the dermis layer 425. When a single THz pulse 427 is reflected fromthe skin, multiple reflections due to the stratum corneum/air interface429, stratum corneum/epidermis interface 431 and the epidermis/dermisinterface 433. The signal from each of these interfaces can be seen inthe output pulse 435.

The data shown in FIGS. 20 to 25 is taken from the human arm shown inFIG. 20. Point a indicates the centre inside forum, point b indicatesthe inside wrist, point c indicates the palm of the hand, point dindicates the side of the hand and point e indicates the secondfingertip. THz radiation is non-ionising and low average powers are used(typically 1 mW). Therefore, brief exposure to it is not thought to behazardous.

FIG. 21a shows a time domain THz waveform obtained from point a on FIG.20. The time domain waveform has been processed in order to remove someunwanted artefacts. The oscillations following the main pulse due toatmospheric water removed by deconvolving the data set with thereference pulse waveform obtained in the absence of the sample. The dataset is also spectrally filtered to remove out of band noise by applyinga band pass filter with pass band adjusted to match that of thereference pulse.

In FIG. 21a , the data for point a is shown as a solid line. This iscompared with a dashed line which shows data for air (measured inabsence of sample) and a dotted line which shows the waveform obtainedfrom a pure water sample.

The THz waveform in the absence of the sample (dashed line) shows agaussian pulse corresponding to reflection from the top surface of thewindow (window-air interface). The width of this gaussian indicates thetemporal resolution obtainable with the technology as determined by theband width of the THz pulse.

The waveform obtained from water is opposite in polarity to theno-sample case as expected for a reflection from a higherrefractive-index dielectric. After the initial transient, water displaysa damped decay back to zero over a period of 1 to 2 ps.

The THz waveform of the forearm from point a displays a positive peak atzero optical delay corresponding to the presence of the relativelydehydrated stratum corneum layer. For delay values greater than this,the THz waveform appears to be substantially similar to that for water.This indicates that there is a high water content in the upper dermallayer. The bandwidth of the system is efficient to a depth resolution ofabout 40 μm into the skin. The stratum corneum of the forearm istypically 10 to 20 μm. The positive peak can be taken as a measure ofthe dehydration volume of the stratum corneum. The stratum corneumthickness cannot be distinguished from the dehydration level in thiscase.

FIG. 21b shows a process waveform for skin at point a (solid line),point b (dashed line) and point c (dotted line). There is littlereproducible difference between the scans for the forearm and the wrist.However, the palm gives significantly different results. In this case,there is a differential feature due to reflection of the stratum coriumsurface followed, at a longer delay time by a broader negative transientdue to the stratum corneum-epidermis interface. This transient displaysthe damp decay to zero expected for the water-like epidermis. Thestratum corneum has a thickness from 100 to 150 μm on the palm of thehand which is thick enough for its inner and outer boundaries to beseparated.

FIGS. 22a and b show images obtained by raster scanning a 1 cm by 1 cmarea of the side of the subject's hand (point d) in FIG. 20.

FIG. 22a is generated by plotting the peak value of the processed THzwaveform corresponding to the outside surface of the stratum corneumalong the z axis (i.e. out of the palm) across the whole 1 cm by 1 cmarea). Typical features of the skin surface (lines, wrinkles etc) areevident. FIG. 22b shows essentially a time slice image where the THzwaveform values at a time delay corresponding to the stratumcorneum-epidermis interface are plotted. This allows variations in thestratum corneum thickness over the scanned area to be seen. (Low xvalues are towards the palm side of the hand while the higher values aretowards the back-side).

In the data of both FIG. 22a and FIG. 22b , the reflected THz waveformsare acquired over a spatial interval of 3 waveforms per millimeter alongthe two axis. This is roughly equivalent to the diffraction limitedresolution achievable in this frequency regime. FIGS. 23a and 23b showslices through a 3D data set. The grey scale indicates the THz amplitudeand is plotted against optical delay (vertical access) and x positionacross the horizontal axis. A depth calibration is obtained from theoptical delay time based on an assumed refractive index of n=2 for skintissues over the THz regime. The figures indicate the stratumcorneum/epidermis interface and also the stratum corneum surface. FIG.23a is taken at point c whereas FIG. 23b is taken at point d.

The sensitivity of THz towards absorption is shown in FIG. 24a . Here,the reflective parts from the forearm of FIG. 20 were measured beforeand at intervals after hydrating the stratum corneum by application ofwater-soaked gauze. Trace “a” shows a THz signal prior to removal of thegauze, trace “b” shows the signal immediately after removal of thegauze. Here, it can be seen that the THz waveform is strongly suppressedat zero optical delay indicating near-saturated hydration of the stratumcorneum and traces “c” to “e” show the same measurement five minutes,ten minutes and fifteen minutes respectively after removal of the gauze.The soaked region of skin is exposed to an ambient atmosphere (23° C.).The zero-delay peak covers over a characteristic time of 15 minutes. Itis interesting to note that although the positive peak covers afterinitial hydration, the following minimum is first reduced in depth byhydration and subsequently increases to become more negative than beforehydration.

FIG. 24b shows the change in the hydration level of the stratum coriumproduced by application of 60 milligrams of 10% glycerine solution. Thedotted line indicates the waveform before the glycerine is applied. Thesolid line shows the waveform 8 minutes after application of thesolution. The upper trace for point “c” (palm) whereas the lower traceis for point “a” (forearm).

The forearm for glycerine results display the same suppression of thezero-delay peak as those achieved using pure water. Actually, thezero-delay peak appears more strongly suppressed than in the pure watercase after five minutes drying time. Indicating the improved retentionof water in the presence of glycerine. Little change is seen in thehydration level of the palm. However, small changes in the features of alater time delay can be seen.

FIG. 25a illustrates the effect of occlusion of the stratum corneuminterface by the quartz window. Here, THz measurements were made at 45second intervals over a 15 minute period with the skin in continuouscontact with quartz. The scans are offset from one another along the xaxis with the later most times to the right. The size of the zero-delaypeak decreases with an exponential decay form.

The peak-to-peak values for each waveform is plotted as a function oftime in FIG. 25b . An exponential decay is fitted to the data. It wasfound that the time-constant for the decay is 3.1 minutes.

The invention claimed is:
 1. A method of imaging a sample, the methodcomprising: irradiating a plurality of points of a surface of the samplewith a pulse of electromagnetic radiation, said pulse having a pluralityof frequencies in the range from 25 GHz to 100 THz; detecting theamplitude of the radiation having a plurality of frequencies in therange from 25 GHz to 100 THz reflected from or transmitted by each pointof the sample as a function of delay time, wherein the delay time is thetime that it takes the radiation to travel through a region of thesample; generating a first two-dimensional image of the points of thesample at a first interface of the sample using an amplitude of theradiation detected for a delay time corresponding to the firstinterface; and generating a second two-dimensional image of the pointsof the sample at a second interface of the sample using an amplitude ofthe radiation detected for a delay time corresponding to the secondinterface; obtaining a depth calibration based on a refractive index;determining variation in thickness of the layer of the sample betweenthe first interface and the second interface from the delay timecorresponding to the first interface and the delay time corresponding tothe second interface.
 2. A method according to claim 1, wherein thefirst interface is an internal dielectric interface or an externalsurface of the sample and the second interface is an internal dielectricinterface or an external surface of the sample.
 3. A method according toclaim 2, wherein the first interface is a first external surface of thesample and the second interface is a second external surface of thesample and determining the variation in thickness of the layer of thesample between the first interface and the second interface comprisesdetermining the variation in the depth of the sample.
 4. An apparatusfor generating an image of a sample, the apparatus comprising: anemitter for irradiating a plurality of points of a surface of a samplewith a pulse of electromagnetic radiation, said pulse having a pluralityof frequencies in the range from 25 GHz to 100 THz; a detector fordetecting the amplitude of the radiation having a plurality offrequencies in the range from 25 GHz to 100 THz reflected from ortransmitted by each point of the sample as a function of delay timewherein the delay time is the time that it takes radiation to travelthrough a region of the sample; and a processor: for generating a firsttwo dimensional image of the points of the sample at a first interfaceof the sample using an amplitude of the radiation detected for a delaytime corresponding to the first interface; for generating a second twodimensional image of the points of the sample at a second interface ofthe sample using an amplitude of the radiation detected for a delay timecorresponding to the second interface; and for obtaining a depthcalibration based on a refractive index and determining variation inthickness of the layer of the sample between the first interface and thesecond interface, from the delay time corresponding to the firstinterface and the delay time corresponding to the second interface. 5.An apparatus according to claim 4, wherein the first interface is aninternal dielectric interface or an external surface of the sample andthe second interface is an internal dielectric interface or an externalsurface of the sample.
 6. A method according to claim 1, wherein thedelay time is measured by varying the phase of a reference beam withrespect to the beam of reflected radiation.
 7. A method according toclaim 1, wherein one of the first image and the second image showfeatures of the sample surface.